The central focus of this book is the control of
continuous-time/continuous-space nonlinear systems. Using new
techniques that employ the max-plus algebra, the author addresses
several classes of nonlinear control problems, including nonlinear
optimal control problems and nonlinear robust/H-infinity control
and estimation problems. Several numerical techniques are employed,
including a max-plus eigenvector approach and an approach that
avoids the curse-of-dimensionality.
Well-known dynamic programming arguments show there is a direct
relationship between the solution of a control problem and the
solution of a corresponding Hamiltona "Jacobia "Bellman (HJB)
partial differential equation (PDE). The max-plus-based methods
examined in this monograph belong to an entirely new class of
numerical methods for the solution of nonlinear control problems
and their associated HJB PDEs; they are not equivalent to either of
the more commonly used finite element or characteristic approaches.
The potential advantages of the max-plus-based approaches lie in
the fact that solution operators for nonlinear HJB problems are
linear over the max-plus algebra, and this linearity is exploited
in the construction of algorithms.
The book will be of interest to applied mathematicians,
engineers, and graduate students interested in the control of
nonlinear systems through the implementation of recently developed
numerical methods. Researchers and practitioners tangentially
interested in this area will also find a readable, concise
discussion of the subject through a careful selection of specific
chapters and sections. Basic knowledge of control theory for
systems with dynamics governed bydifferential equations is
required.
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